Amazing post
@Den_Den_Mushi.
Let me add a tad bit.
Mihawk at the time of his introduction comes off as an overwhelmingly powerful individual who exudes badass-ery, is supercilious to everyone around, and just doesn't care about anything. At the beginning of the duel between him and Zoro, Zoro is nothing more than just another random nobody, who Mihawk perceives as a ''frog in the well'' someone who after seeing the difference in power will just run.
However, Zoro shows off his conviction and that captivates Mihawk enough, possibly even reminds him of his younger self. This intrigues Mihawk and even makes him smile, something rarely seen. The subtle change indicates that Mihawk has respect for others, and even shows care for them. He respected Zoro's conviction, respected him as a swordsman, gave him the cut over his chest out of respect. He is mesmerized by his dedication to the swordsmen code.
He is even seen reading the news about Zoro and Luffy.
What many people often forget about Mihawk is that he is essentially one of the few rare winners of One Piece, someone who has completely achieved his dream. He is at the top of the world, without a challenge and that is the cause of his boredom. We see Mihawk at the end of his journey when he is the WSS, so many cannot correlate with him. That's why to some he seems like a bland character. That's why we are following Zoro on his way to the WSS, to see all the sacrifices, all the necessary things one must go through. With Mihawk we have a ''done deal'' per se, so sometime it's hard to sympathize with that for some people. But we also see more of Mihawk's character after his interaction with Zoro and Perona, which you have already magnificently covered, so I have nothing to add. Mihawk will also have his second dream fulfilled. Finding someone worthy and someone giving him the much coveted challenge he seeks for.
Also besides them, Mihawk has a good relationship with Shanks as well, even though they have had ruthless duels in the past and Shanks implying they might have scarred each other, and scars in OP represent big things.
Mihawk deems it necessary to extend his apologies to Shanks in case Luffy cannot survive him.
Mihawk remembered the story Shanks told him quite a long ago.
Mihawk also stays and drinks with Shanks to celebrate.
So yeah, Mihawk is quite an interesting character, that is most often overlooked.
At the end I will leave this hype pic of Mihawk. And I am looking forward to his next appearance and what it will bring.